Optimal Design of Level-1 Redundant Water Distribution Networks with Fuzzy Demands

A WDN capable of sustaining failure of any one pipe without causing disruption in services either in full or part is considered as the level-1 redundant network. Unknown future water demands are treated as fuzzy parameters using fuzzy logic technique. Fuzzy optimization model is formulated for design of level 1 redundant WDN considering fuzzy demands. Fuzzy nodal demands are characterized by triangular membership functions. For each node, membership function for the available nodal heads is also considered to be approximately represented by triangular membership function. Furthermore, desirable nodal heads are also considered fuzzy. Relationship between fuzzy available nodal heads and fuzzy desirable nodal heads is used to convert fuzzy constraints to crisp constraints. Genetic algorithm that can easily consider multiple demand scenarios for various pipe failure conditions is used for determining the optimal design cost. The proposed methodology has been illustrated with an example network.